NCERT Solutions Ganita Prakash Chapter 6 Matha Pachchi! — Figure it Out
Book page 133 Updated on2026-09-05
Q1.
Find out the total distance Akshi has covered in 5 rounds.
Answer
Akshi runs on the outer track, which is a rectangle 70 m long and 40 m wide.
One round = 2 × (70 m + 40 m) = 2 × 110 m = 220 m
5 rounds = 5 × 220 m = 1100 m
Answer: Akshi covered 1100 m (1 km 100 m).
Q2.
Find out the total distance Toshi has covered in 7 rounds. Who ran a longer distance?
Answer
Toshi runs on the inner track, which is 60 m long and 30 m wide.
One round = 2 × (60 m + 30 m) = 2 × 90 m = 180 m
7 rounds = 7 × 180 m = 1260 m
Now compare the two totals:
Toshi 1260 m > Akshi 1100 m
1260 − 1100 = 160 m
Answer: Toshi ran the longer distance — 160 m more than Akshi, even though her track is smaller. She simply ran two more rounds.
Math Talk: A smaller track does not mean a smaller distance. What matters is perimeter × number of rounds.
Q3.
Think and mark the positions as directed— a. Mark ‘A’ at the point where Akshi will be after she ran 250 m. b. Mark ‘B’ at the point where Akshi will be after she ran 500 m. c. Now, Akshi ran 1000 m. How many full rounds has she finished running around her track? Mark her position as ‘C’. d. Mark ‘X’ at the point where Toshi will be after she ran 250 m. e. Mark ‘Y’ at the point where Toshi will be after she ran 500 m. f. Now, Toshi ran 1000 m. How many full rounds has she finished running around her track? Mark her position as ‘Z’.
Answer
Both girls start at the bottom-right corner of their own track and run along the bottom side first, then up the left side, then along the top, then down the right side. Each time, divide the distance by one round and use the remainder to walk around the track.
Akshi — one round = 220 m
a. 250 = 220 + 30 → 1 full round, then 30 m more A lies on the bottom (70 m) side, 30 m from her starting corner.
b. 500 = 2 × 220 + 60 → 2 full rounds, then 60 m more B lies on the bottom side, 60 m from the start (10 m short of the corner).
c. 1000 = 4 × 220 + 120 → 4 full rounds, then 120 m more
120 = 70 (bottom) + 40 (left side) + 10 → C lies on the top side, 10 m from the top-left corner.
Toshi — one round = 180 m
d. 250 = 180 + 70 → 70 = 60 (bottom) + 10 X lies on the left (30 m) side, 10 m above the bottom-left corner.
e. 500 = 2 × 180 + 140 → 140 = 60 + 30 + 50 Y lies on the top side, 50 m from the top-left corner.
f. 1000 = 5 × 180 + 100 → 5 full rounds, then 100 = 60 + 30 + 10 Z lies on the top side, 10 m from the top-left corner.
The two tracks with every marked position. A and B are on Akshi's bottom side; C, Y and Z are on the top sides; X is on Toshi's left side.
Why division with remainder works: after each full round the runner is back at her starting point. So only the remainder decides where she stops.